Determining the impulse characteristic of a stable linear element.(English. Russian original)Zbl 0696.93020

Sov. Phys., Dokl. 34, No. 2, 89-90 (1989); translation from Dokl. Akad. Nauk SSSR 304, No. 6, 1312-1314 (1989).
For a stable linear element described by $$z(t)=\int^{t}_{0}K(s)u(t- s)ds$$, where K(t) is the impulse response and z(t) is the output, the input $$u(t)=\sin (at^ 2+bt)$$, $$t\geq 0$$, is considered (a,b being suitable constants). It is shown that, under certain conditions, $$H(t;a)=(4a/\pi)\int^{\infty}_{0}z(\tau)\sin [a(\tau -t)^ 2+b(\tau -t)]d\tau$$ is an estimate of K(t), i.e. $$\lim_{a\to \infty}| H(t;a)-K(t)| =0$$ uniformly on each finite time interval. Similar results are obtained for the cases when the excitation/observation time is finite and/or z(t) is unavoidable altered by measuring errors.
Reviewer: M.Voicu

MSC:

 93B30 System identification 93C30 Control/observation systems governed by functional relations other than differential equations (such as hybrid and switching systems) 44A35 Convolution as an integral transform